I know lots of people know this anecdote, but it's a good one!

Christopher Sims October 21, 1942 – March 14, 2026 youtube.com/watch?v=3JMwAtON…

Thanks for the engagement and the thoughtful response. It is difficult to outline my (many) points of agreement and the few points where I differ in an X post, but I will try. > "I've never insisted on the "frequency interpretation" of probability." In this paper statistical analysis is defined in frequentist terms. escholarship.org/content/qt4… I acknowledge I am being particularly purist here, but to a strict (operational subjective) Bayesian, probability does not exist, and the idea of a Bayesian estimator is a contradiction in terms. The concept of "experimental conditions remaining the same" only makes sense with a frequentist notion of repeated draws from a low-dimensional probability model.

Full talk here: youtube.com/watch?v=hoFRVJLn… Papers: arxiv.org/abs/1906.07125 proceedings.mlr.press/v163/r… ICML Position paper by @kayembruno openreview.net/pdf?id=V1FP9W… which independently makes a similar argument.

To Pearl the probability is the "model" g(x|θ) but to a strict Bayesian it is P(x1,..,xn).

@yudapearl 's insistence that Bayesian causality and probabilistic causality is an oxymoron is based upon frequentist probability.

and secondly:

Simpson's paradox adds a covariate to the problem, in this case there are two different conditionally exchangeable models that (if agreed upon) would result in straight forward inference and consensus, but they are quite different from each other. Firstly:

Applying Bayes rule, the conditional probability of y* given the historical data y1,..yn,t1,..tn and the treatment is given by the following which reduces to just a Bayesian regression:

Let's shift to a problem involving causality, as well as observing y1,..yn,t1,..,tn there will also be the outcome of a treatment on a future unit y* and the treatment on that unit t*, because t* is set by us it isn't random and has no distribution. One possible representation of probabilistic belief is given by the following application of the de Finetti representation also applying the 'regression assumption'.